Linear codes from perfect nonlinear mappings and their secret sharing schemes

Author

Carlet, Claude ; Ding, Cunsheng ; Yuan, Jin

Author_Institution

INRIA, France

Volume

51

Issue

6

fYear

2005

fDate

6/1/2005 12:00:00 AM

Firstpage

2089

Lastpage

2102

Abstract

In this paper, error-correcting codes from perfect nonlinear mappings are constructed, and then employed to construct secret sharing schemes. The error-correcting codes obtained in this paper are very good in general, and many of them are optimal or almost optimal. The secret sharing schemes obtained in this paper have two types of access structures. The first type is democratic in the sense that every participant is involved in the same number of minimal-access sets. In the second type of access structures, there are a few dictators who are in every minimal access set, while each of the remaining participants is in the same number of minimal-access sets.

Keywords

Galois fields; cryptography; error correction codes; linear codes; access structure; cryptography; error-correcting code; linear code; minimal-access set; nonlinear mapping; planar function; secret sharing scheme; Authentication; Computer science; Councils; Cryptography; Error correction codes; Information rates; Linear code; Cryptography; linear codes; perfect nonlinear functions; planar functions; secret sharing schemes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2005.847722

Filename

1435652